What is the answer to 2ix+3=y-i ?

The answer to 2ix+3=y-i is x=-1/2 ,y=3

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2ix+3=y-i

2 i x + 3 = y - i

x = - \frac{1}{2}, y = 3

Solution steps

2 i x + 3 = y - i

Rewrite

2 i x + 3

in standard complex form:

3 + 2 x i

3 + 2 x i = y - i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[3 = y 2 x = - 1]

[3 = y 2 x = - 1] : x = - \frac{1}{2}, y = 3

x = - \frac{1}{2}, y = 3

2 + 3 i = x + y i

(x + y i)^{2} - 3 i (x + y i) + 5 i = 0

x^{2} + 8 i = 0

2 i x^{2} + x + 3 i = 0

w^{2} - i (w - 2) = (w - 2)